Graph Drawing via Gradient Descent, (GD)

Readability criteria, such as distance or neighborhood preser1 vation, are often used to optimize node-link representations of graphs to 2 enable the comprehension of the underlying data. With few exceptions, 3 graph drawing algorithms typically optimize one such criterion, usually 4 at the expense of others. We propose a layout approach, Graph Drawing 5 via Gradient Descent, (GD), that can handle multiple readability crite6 ria. (GD) can optimize any criterion that can be described by a smooth 7 function. If the criterion cannot be captured by a smooth function, a 8 non-smooth function for the criterion is combined with another smooth 9 function, or auto-differentiation tools are used for the optimization. Our 10 approach is flexible and can be used to optimize several criteria that 11 have already been considered earlier (e.g., obtaining ideal edge lengths, 12 stress, neighborhood preservation) as well as other criteria which have 13 not yet been explicitly optimized in such fashion (e.g., vertex resolution, 14 angular resolution, aspect ratio). We provide quantitative and qualitative 15 evidence of the effectiveness of (GD) with experimental data and a func16 tional prototype: http://hdc.cs.arizona.edu/~mwli/graph-drawing/. 17